In the past decades,
there has been a large amount of research denoted to energy-stable numerical schemes for time discretization of gradient flow equations,
such as convex splitting schemes [1]}, [2]}, [3]},
stabilized semi-implicit schemes [4]}, [5]}, [6]},
and exponential time differencing (ETD) schemes [7]}, [8]}, [9]}.
More recently, invariant energy quadratization (IEQ) schemes [10]}, [11]}, [12]}
and scalar auxiliary variable (SAV) schemes [13]}, [14]}, [15]}
were proposed to naturally provide energy-stable and linear algorithms with second-order temporal accuracy.
While the main idea for both methods is to reformulate and split the energy functional (REF ) in the quadratic form by introducing extra variables, the SAV approach is usually more efficient in terms of computations.
Many variants of SAV schemes were developed later;
see [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]} and the references therein.
In practice, a suitable stabilization term is also introduced in such splitting in order to maintain numerical stability
for highly stiff problems. On the other hand, existing SAV-type schemes usually fail to preserve the MBP, and a special case is the auxiliary variable proposed in [21]} which is shown to be positivity-preserving.
